The present invention relates generally to the use of nonlinear optical effects for characterization of ultrashort (optical pulse duration .tau.&lt;10.sup.-10 seconds) laser pulses, and, more particularly, to apparatus and methods for such characterization utilizing third-order frequency-resolved optical grating (FROG) techniques.
Advances in laser technology have required corresponding advances in optical diagnostic and characterization methods and apparatus. For example, as the pulse width available to technology entered the picosecond and sub-picosecond regime, the ability of conventional optoelectronic techniques, such as electrically recorded light-sensitive diodes or electronic streak cameras, to record and characterize such ultrashort pulses became quite limited.
In response, a class of purely optical techniques for measuring extremely short optical pulses has evolved. These techniques may be described as gating techniques, wherein a light pulse of known characteristics and controllable time delay is used, generally through nonlinear optical effects, to control the light coming from an unknown optical pulse. As the time delay is varied, different parts of the unknown optical pulse are allowed to pass through the gate. Measurement of the amount of light which so passes can be measured by optoelectronic means, even when the pulse duration is shorter than the temporal resolution of the sensor. By varying the time delay, it is thereby possible to determine, for example, the duration and relative intensity of an unknown optical pulse.
Considerably more information resides in an optical pulse, however. An ultrashort laser pulse, rather than being monochromatic, is spread over a spectral range. The extent of such broadening is on the order of .DELTA..omega./.omega..about.1/.omega..tau., where .DELTA..omega. is the width of the spectral range found in the optical pulse, .omega. is the average frequency of the optical pulse, and .tau. is the duration of the optical pulse. For example, if .omega.=6.times.10.sup.14 Hz (blue light) and .tau.=10 femtoseconds, then the fractional bandwidth .DELTA..omega./.omega. is .about.0.16. Such an optical pulse thus contains photons ranging in frequency (nominally) from .about.5.times.10.sup.14 Hz (green) to .about.7.times.10.sup.14 Hz (violet).
A great deal of information concerning the pulse shape, phase, polarization, and other factors of interest are encoded in the time-dependent spectrum of the optical pulse. A class of techniques which may be termed spectrally-sensitive gating techniques have been developed to make this information accessible. The basic idea is to measure the spectrum of an optically-gated pulse as a function of the time delay, thereby obtaining time-resolved spectral information describing the optical pulse.
One approach to implementing spectrally-sensitive gating are frequency-resolved optical grating (FROG) based techniques, which are known to be capable of directly obtaining intensity and phase information concerning an ultrashort optical pulse. In the simplest form, an input light pulse is formed into a probe pulse. A gate pulse is provided (derived either from the probe pulse or from a separate beam) having a variable delay relative to the probe pulse. The gate pulse and the probe pulse are then combined in a nonlinear medium to form a signal pulse representing the probe pulse characteristics at a time functionally related to the delay of the gate pulse, thereby providing a series of temporal slices of the probe pulse. A spectrometer receives the output pulse to generate an intensity signal as a function of delay and wavelength.
Numerous FROG-based techniques for characterizing optical pulses exist. The gate pulse can be delayed with various values to provide a plot of signal intensity vs. wavelength and gate pulse delay. Alternatively, the gate pulse and probe pulse can be propagated through the nonlinear element at an angle to output a signal having a linear range of gate pulse delay times vs. position that directly yields the plot of signal intensity vs. wavelength and gate pulse delay on a single pulse without the need for a variable delay. These and related techniques, and the procedures to recover the intensity and phase information from the time-dependent spectral information provided thereby, are well-known in the art.
It will be useful to describe a particular implementation of the FROG technique in somewhat greater detail. Two pulses, a gate pulse and a signal pulse, are generated. The goal is to measure the intensity I(t) and the phase .phi.(t) of the signal pulse. The gate pulse shall be taken as identical to the signal pulse, save for a variable time delay. This can be accomplished as indicated in FIG. 1, wherein an input pulse 100 is split by beamsplitter 101 into a gate pulse 102 and a signal pulse 103. A time delay .tau. is applied to gate pulse 102 by delay line 104, which pulse is then recollimated with signal pulse 103 by mirror 105.
The gate pulse 102 and the signal pulse 103 are combined in a nonlinear optical medium 107, often through the action of a focusing lens 108 which serves to increase the interacting electric fields by concentrating the light onto a small spatial region, thereby increasing the quantum efficiency of the nonlinear optical effect being utilized. For simplicity, this nonlinear optical medium should have a response that is faster than the duration of the optical pulse to be measured. We shall refer to such nonlinear optical materials as responding instantaneously. An output pulse 109 is thereby generated.
The electric fields for an output pulse generated using the second-harmonic generation effect are given by EQU E.sub.out (t,.tau.).varies.E(t)E(t-.tau.);
in which t is the time, .tau. is the delay, and E(t) is the electric field of the gate and signal pulses (earlier assumed identical save for a time delay of .tau. for simplicity). Although a second-order nonlinear effect is used in this illustration, nonlinear optical effects of any order can be used to implement FROG techniques.
Output signal 109 is directed into a spectrometer 110, wherein the spectrum of the output signal is measured as a function of the time delay .tau. between gate pulse 102 and signal pulse 103. The measured signal I.sub.out is a function of frequency .omega. and delay .tau.: EQU I.sub.out (.omega.,.tau.).varies..vertline..intg.E.sub.out (t,.tau.)exp(-i.omega.t)dt.vertline..sup.2
The resulting problem is mathematically similar to the two-dimensional phase-retrieval problem, which is known to have an essentially unique solution. Numerous analytical and numerical techniques for finding this solution are known in the art.
FROG-based techniques are particularly adapted to single shot measurements as well as the analysis of multi-shot pulse trains. The term ultrashort is used to refer to pulse durations shorter than about 100 picoseconds. This identifies the regime in which FROG techniques are particularly useful owing to the failure of conventional techniques. However, there is no fundamental restriction to ultrashort pulses, as straightforward adaptation of the FROG techniques may be made to measure optical pulses of any duration desired. There is also no fundamental limit to the wavelengths which may he analyzed using FROG-based techniques. Any limitations which appear in practice are those associated with the detectors and spectrometers available, thus offering the possibility of using FROG-based techniques in the vacuum UV and x-ray regions of the spectrum when suitable detectors and nonlinear materials become available. Finally, although the present discussion is in terms of ultrashort laser pulses, no fundamental restriction to pulses originating from laser sources is intended.
State-of-the-art FROG techniques, flexible as they are, have limitations which restrict their application in a variety of potentially useful applications. Perhaps the most significant limitation is that associated with the use of second-order nonlinear optical effects. Such effects are generally used because of the relatively high quantum efficiency associated therewith. However, second-order nonlinear optical effects are blind to the direction of time. This insensitivity raises the possibility of false and misleading characterization of optical pulse shape and phase.
Adoption of gated third-order nonlinear effects would result in regaining the direction of time, thereby producing data containing more information about the pulse. (As a useful extra, third-order data is also much easier to interpret.) The disadvantage of using third-order nonlinear effects in FROG-based optical pulse analysis is that the quantum efficiency of such processes is dramatically smaller than that for second-order processes, thereby severely limiting the applicability of such techniques.
We address this perceived need by introducing new FROG-based diagnostic techniques which allow the use of third-order nonlinear optical processes in practical measurement of ultrashort optical pulses. These techniques enhance the production of a third-order nonlinear optic signal by either increasing the effective interaction length within which this effect is produced, or by using the phenomenon of interface-enhanced third-harmonic generation, which also reduces the background light that can interfere with the optic signal. Various embodiments and other features, aspects, and advantages of the present invention will become better understood with reference to the following description and appended claims.